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ardnaxella
@ardnaxella
July 2022
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7sin²x+4sin2x=7cos²x
помогите)
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nafanya2014
Verified answer
4sin2x=7cos²x-
7sin²x
4sin2x=7·(cos²x-
sin²x)
4sin2x=7·cos2x
Делим на сos2x≠0
tg2x=7/4
2x=arctg(7/4)+πk, k∈Z
x=(1/2)
arctg(7/4)+(π/2)·k, k∈Z
или
7sin²x+4·2sinx·cosx-7cos²x=0
Делим на cos²x≠0
7tg²x+8tgx-7=0
D=64-4·7·(-7)=64+196=260
tgx=(-8-2√65)/14 или tgx=(-8+2√65)/14
tgx=(-4-√65)/7 или tgx=(-4+√65)/7
х=artcg(-4-√65)/7 + πn, n∈Z или х=artcg(-4+√65)/7 + πm, m∈Z
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Answers & Comments
Verified answer
4sin2x=7cos²x-7sin²x4sin2x=7·(cos²x-sin²x)
4sin2x=7·cos2x
Делим на сos2x≠0
tg2x=7/4
2x=arctg(7/4)+πk, k∈Z
x=(1/2)arctg(7/4)+(π/2)·k, k∈Z
или
7sin²x+4·2sinx·cosx-7cos²x=0
Делим на cos²x≠0
7tg²x+8tgx-7=0
D=64-4·7·(-7)=64+196=260
tgx=(-8-2√65)/14 или tgx=(-8+2√65)/14
tgx=(-4-√65)/7 или tgx=(-4+√65)/7
х=artcg(-4-√65)/7 + πn, n∈Z или х=artcg(-4+√65)/7 + πm, m∈Z